Antenna Theory

This book introduces the fundamental principles of antenna theory and explains how to apply them to the analysis, design, and measurements of antennas. Due to the variety of methods of analysis and design, and the different antenna structures available, the applications covered in this book are made to some of the most basic and practical antenna configurations. Among these antenna configurations are linear dipoles; loops; arrays; broadband antennas; aperture antennas; horns; microstrip antennas; and reflector antennas. The text contains sufficient mathematical detail to enable undergraduate and beginning graduate students in electrical engineering and physics to follow the flow of analysis and design. Readers should have a basic knowledge of undergraduate electromagnetic theory, including Maxwell’s equations and the wave equation, introductory physics, and differential and integral calculus. ^[1] 

Table of Contents

Preface xiii

About the Companion Website xix

1 Antennas 1

1.1 Introduction 1

1.2 Types of Antennas 3

1.3 Radiation Mechanism 7

1.4 Current Distribution on a Thin Wire Antenna 15

1.5 Historical Advancement 18

1.6 Multimedia 21

References 22

2 Fundamental Parameters and Figures-of-Merit of Antennas 25

2.1 Introduction 25

2.2 Radiation Pattern 25

2.3 Radiation Power Density 35

2.4 Radiation Intensity 37

2.5 Beamwidth 40

2.6 Directivity 41

2.7 Numerical Techniques 55

2.8 Antenna Efficiency 60

2.9 Gain, Realized Gain 61

2.10 Beam Efficiency 65

2.11 Bandwidth 65

2.12 Polarization 66

2.13 Input Impedance 75

2.14 Antenna Radiation Efficiency 79

2.15 Antenna Vector Effective Length and Equivalent Areas 81

2.16 Maximum Directivity and Maximum Effective Area 86

2.17 Friis Transmission Equation and Radar Range Equation 88

2.18 Antenna Temperature 96

2.19 Multimedia 100

References 103

Problems 105

3 Radiation Integrals and Auxiliary Potential Functions 127

3.1 Introduction 127

3.2 The Vector Potential A for an Electric Current Source J 128

3.3 The Vector Potential F for A Magnetic Current Source M 130

3.4 Electric and Magnetic Fields for Electric (J) and Magnetic (M) Current Sources 131

3.5 Solution of the Inhomogeneous Vector Potential Wave Equation 132

3.6 Far-Field Radiation 136

3.7 Duality Theorem 137

3.8 Reciprocity and Reaction Theorems 138

References 143

Problems 143

4 Linear Wire Antennas 145

4.1 Introduction 145

4.2 Infinitesimal Dipole 145

4.3 Small Dipole 155

4.4 Region Separation 158

4.5 Finite Length Dipole 164

4.6 Half-Wavelength Dipole 176

4.7 Linear Elements Near or On Infinite Perfect Electric Conductors (PEC), Perfect Magnetic Conductors (PMC) and Electromagnetic Band-Gap (EBG) Surfaces 179

4.8 Ground Effects 203

4.9 Computer Codes 216

4.10 Multimedia 216

References 218

Problems 220

5 Loop Antennas 235

5.1 Introduction 235

5.2 Small Circular Loop 236

5.3 Circular Loop of Constant Current 250

5.4 Circular Loop with Nonuniform Current 259

5.5 Ground and Earth Curvature Effects for Circular Loops 268

5.6 Polygonal Loop Antennas 269

5.7 Ferrite Loop 270

5.8 Mobile Communication Systems Applications 272

5.9 Multimedia 272

References 275

Problems 277

6 Arrays: Linear, Planar, and Circular 285

6.1 Introduction 285

6.2 Two-Element Array 286

6.3 N-Element Linear Array: Uniform Amplitude and Spacing 293

6.4 N-Element Linear Array: Directivity 312

6.5 Design Procedure 318

6.6 N-Element Linear Array: Three-Dimensional Characteristics 319

6.7 Rectangular-to-Polar Graphical Solution 322

6.8 N-Element Linear Array: Uniform Spacing, Nonuniform Amplitude 323

6.9 Superdirectivity 345

6.10 Planar Array 348

6.11 Design Considerations 360

6.12 Circular Array 363

6.13 Multimedia 367

References 367

Problems 368

7 Antenna Synthesis and Continuous Sources 385

7.1 Introduction 385

7.2 Continuous Sources 386

7.3 Schelkunoff Polynomial Method 387

7.4 Fourier Transform Method 392

7.5 Woodward-Lawson Method 398

7.6 Taylor Line-Source (Tschebyscheff-Error) 404

7.7 Taylor Line-Source (One-Parameter) 408

7.8 Triangular, Cosine, and Cosine-Squared Amplitude Distributions 415

7.9 Line-Source Phase Distributions 416

7.10 Continuous Aperture Sources 417

7.11 Multimedia 420

References 420

Problems 421

8 Integral Equations, Moment Method, and Self and Mutual Impedances 431

8.1 Introduction 431

8.2 Integral Equation Method 432

8.3 Finite Diameter Wires 439

8.4 Moment Method Solution 448

8.5 Self-Impedance 455

8.6 Mutual Impedance Between Linear Elements 463

8.7 Mutual Coupling in Arrays 474

8.8 Multimedia 480

References 480

Problems 482

9 Broadband Dipoles and Matching Techniques 485

9.1 Introduction 485

9.2 Biconical Antenna 487

9.3 Triangular Sheet, Flexible and Conformal Bow-Tie, and Wire Simulation 492

9.4 Vivaldi Antenna 496

9.5 Cylindrical Dipole 500

9.6 Folded Dipole 505

9.7 Discone and Conical Skirt Monopole 512

9.8 Matching Techniques 513

9.9 Multimedia 523

References 524

Problems 525

10 Traveling Wave and Broadband Antennas 533

10.1 Introduction 533

10.2 Traveling Wave Antennas 533

10.3 Broadband Antennas 549

10.4 Multimedia 580

References 580

Problems 582

11 Frequency Independent Antennas, Antenna Miniaturization, and Fractal Antennas 591

11.1 Introduction 591

11.2 Theory 592

11.3 Equiangular Spiral Antennas 593

11.4 Log-Periodic Antennas 598

11.5 Fundamental Limits of Electrically Small Antennas 614

11.6 Antenna Miniaturization 619

11.7 Fractal Antennas 627

11.8 Multimedia 633

References 633

Problems 635

12 Aperture Antennas 639

12.1 Introduction 639

12.2 Field Equivalence Principle: Huygens’ Principle 639

12.3 Radiation Equations 645

12.4 Directivity 648

12.5 Rectangular Apertures 648

12.6 Circular Apertures 667

12.7 Design Considerations 675

12.8 Babinet’s Principle 680

12.9 Fourier Transforms in Aperture Antenna Theory 684

12.10 Ground Plane Edge Effects: The Geometrical Theory of Diffraction 702

12.11 Multimedia 707

References 707

Problems 709

13 Horn Antennas 719

13.1 Introduction 719

13.2 E-Plane Sectoral Horn 719

13.3 H-Plane Sectoral Horn 733

13.4 Pyramidal Horn 743

13.5 Conical Horn 756

13.6 Corrugated Horn 761

13.7 Aperture-Matched Horns 766

13.8 Multimode Horns 769

13.9 Dielectric-Loaded Horns 771

13.10 Phase Center 773

13.11 Multimedia 774

References 775

Problems 778

14 Microstrip and Mobile Communications Antennas 783

14.1 Introduction 783

14.2 Rectangular Patch 788

14.3 Circular Patch 815

14.4 Quality Factor, Bandwidth, and Efficiency 823

14.5 Input Impedance 826

14.6 Coupling 827

14.7 Circular Polarization 830

14.8 Arrays and Feed Networks 832

14.9 Antennas for Mobile Communications 837

14.10 Dielectric Resonator Antennas 847

14.11 Multimedia 858

References 862

Problems 867

15 Reflector Antennas 875

15.1 Introduction 875

15.2 Plane Reflector 875

15.3 Corner Reflector 876

15.4 Parabolic Reflector 884

15.5 Spherical Reflector 920

15.6 Multimedia 923

References 923

Problems 925

16 Smart Antennas 931

16.1 Introduction 931

16.2 Smart-Antenna Analogy 931

16.3 Cellular Radio Systems Evolution 933

16.4 Signal Propagation 939

16.5 Smart Antennas’ Benefits 942

16.6 Smart Antennas’ Drawbacks 943

16.7 Antenna 943

16.8 Antenna Beamforming 946

16.9 Mobile Ad hoc Networks (MANETs) 960

16.10 Smart-Antenna System Design, Simulation, and Results 964

16.11 Beamforming, Diversity Combining, Rayleigh-Fading, and Trellis-Coded Modulation 972

16.12 Other Geometries 975

16.13 Multimedia 976

References 976

Problems 980

17 Antenna Measurements 981

17.1 Introduction 981

17.2 Antenna Ranges 982

17.3 Radiation Patterns 1000

17.4 Gain Measurements 1003

17.5 Directivity Measurements 1010

17.6 Radiation Efficiency 1012

17.7 Impedance Measurements 1012

17.8 Current Measurements 1014

17.9 Polarization Measurements 1014

17.10 Scale Model Measurements 1019

References 1024

Appendix I: f (x)= sin(x) x 1027

Appendix II: fN(x)= |||| sin(Nx) N sin(x) |||| N =1, 3, 5, 10, 20 1029

Appendix III: Cosine and Sine Integrals 1031

Appendix IV: Fresnel Integrals 1033

Appendix V: Bessel Functions 1035

Appendix VI: Identities 1041

Appendix VII: Vector Analysis 1045

Appendix VIII: Method of Stationary Phase 1055

Appendix IX: Television, Radio, Telephone, and Radar Frequency Spectrums 1061

Index 1065

Constantine A. Balanis received his BSEE degree from the Virginia Tech in 1964, his MEE degree from the University of Virginia in 1966, his PhD in Electrical Engineering from The Ohio State University in 1969, and an Honorary Doctorate from the Aristotle University of Thessaloniki in 2004. From 1964 to 1970, he was with the NASA Langley Research Center in Hampton, VA, and from 1970 to 1983, he was with the Department of Electrical Engineering of West Virginia University. In 1983 he joined Arizona State University and is now Regents' Professor of Electrical Engineering. Dr. Balanis is also a life fellow of the IEEE.